Oops, no, you messed up.
The brain is part of biology.
If you post the objectively factual statement that "a trans woman is morphologically male (prior to any gender-affirming medical intervention)" or "a trans woman is cytogenetically male" or something like that, do you get the same reaction?
People should object to the statement as stated, because although you might find no differences in visible morphology, some trans people, at least, have very strong gender dysphoria. Without having good evidence that this doesn't have a biological basis, we should assume strong gender dysphoria does since it is akin to lots of other instincts and feelings we have that are innate.
So it's entirely possible that a trans woman is biologically cognitively male, and a trans man is biologically cognitively female. It's also possible that "it's complicated", or that there are differences between different cases that we lump together under being "trans". Actually, given how biology works, it's pretty much a given that there are differences.
Anyway, there are two scenarios to distinguish:
(1) A rare aspect of being biologically male is getting confused, in some sense, and identifying as female, even though you're 100% male in all ways (and vice versa with trans men)--sort of a software glitch.
(2) A rare aspect of neural development is genotypically male individuals cognitively developing as females at least to the extent of self-identity (and vice versa with trans women)--sort of a hardware glitch.
In the former case, trans women are biologically male. In the latter case, they're not. In an in between case, they're also not biologically male, but we also shouldn't overstate how biologically (cognitively) female they are.
(Also, aside: because people imply things by virtue of stating them rather than not, especially when the thing being stated is obvious (why state the obvious?), it's entirely possible and appropriate for people to be upset at you saying true things. For instance, it is hard to imagine anything more true than, "You are going to die, of old age if nothing else gets you first." However, if you keep repeating it to someone, they have every right to object vehemently to the implicit but extremely strong message you're sending by repeatedly mentioning their mortality.)